The France full back is set to play his final match for Arsenal in Saturday's FA Cup final before he begins negotiations with the newly-crowned Premier League champions
As revealed by Goal, the Frenchman has told Arsenal he will not sign a new contract and will leave at the end of the season.
He let manager Arsene Wenger know at the end of last week that the FA Cup final against Hull City on Saturday will be his final game for the Gunners.
Sagna has attracted strong interest from Premier League big-hitters as well as clubs on the continent, including Chelsea, Liverpool and Paris Saint-Germain.
But newly-crowned Premier League champion City is believed to be in pole position to capture the versatile full back.
Manuel Pellegrini’s team is ready to offer Sagna a 100,000 pound-a-week deal spread over three years, even though his premier position at right back is the same as that of Pablo Zabaleta, one of City’s best players this season.
Arsenal had been close to an agreement with Sagna last month after offering him an 80,000 pound-a-week, two-year deal with the option of a third year in a final attempt to keep him at the club.
However, the 31-year-old has rejected the offer and he will end his seven-year spell at Emirates Stadium after Saturday's final.
The right back is believed to be settled with his family in England and is keen to remain in the Premier League.
Losing Sagna will be a blow to Arsene Wenger, with the player offering experience and versatility that is not easy to replace. He filled in at center back against Norwich City on Saturday as Wenger chose to rest Per Mertesacker ahead of the cup final.
Toulouse's Serge Aurier is currently top of Arsenal’s target list to replace Sagna. Goal revealed on Tuesday that the Gunners have opened preliminary talks with the Ligue 1 club about a 7 million pound summer move for the Ivory Coast international, 21.
The defender, who turned 31 in February, is able to join another club on a free transfer on July 1.